Background

Goal: Explore the effect of the size of the gene pool (i.e., genetic diversity) on response of the population to an IRS intervention.

Seasonality is incorporated into the dynamics.

IRS: IRS is applied yearly from the end of the dry sesaon to the end of the wet season (days 120-300), with a 90% coverage. The intervention increases the mortality of adult hosts and is implemented with a deterministic model.

Design:

Each combination of factors has 10 runs.

I also ran low transmission, this is not presented here.

Example of a full time series

This example is for: Immune selection with gene pool size of 12000 with no IRS (control; black) and 5-year IRS (green). The time series shows that while transmission recovers to pre-intervention levels (n_total_bites), the diversity (n-alleles, n_circulating_genes, n_circulating_strains) and epidemiology (meanMOI, prevalence) do not.

Compare between experiments for a given diversity

This is a more detailed comparison for the same level of diversity for the four experiments.

Comparison of different genetic pool sizes for a given experiment

This is an example with a 5-year IRS. The higher the diversity, the weaker the effect of the IRS, especially on prevalence.

Time to extinction as a function of the diversity

Some of the time series went extinct before the intervention was lifted. This can be quantified by the time the simulations ended. Those that have not reached the end (40,000 days) went extinct. Of those which went extinct, different runs end at different times. I quantified the maximum (red) and mean (blue) time of the runs.

In general, higher diversity promotes survival through an intervention. Although I expected a monotonic increase of time to extinction with diversity, this did not seem to be the case.

Probability of extinction as a proportion of runs which went extinct

Because not all runs went extinct, I quantified the ability to survive IRS as the proportion of runs that went extinct (should be 0 for control). One expects a higher proportion in a stronger IRS and lower diversity. This is the general trend although again, the expected monotnic relationship between diversity and extinction probablty is absent.

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Quantify effect of IRS compared to control

Full time series

To better quantify the effect of diversity, I calculated by what proportion IRS affected a given measure (e.g., prevalence, number of repertoires). Note that this is done on a time-point basis, and therefore compared to control. This is because the control experiment quantifies the value of a variable at a given time had IRS not been employed. The figure below shows an example for diversity of 12000, with 5-year IRS. This is essentially the difference between the time series in the first figure in this document.

Summary across diversity levels

This previous figure can be summarized by calculating the ratio between the pre- and post-IRS for any given measure (e.g., prevalence). For example, one can say that intervention has reduced the prevalence by 50% compared to control. For this comparison, I first calculate the ratio between the control and experiment at any given time point post-IRS, and then I take the mean of that ratio to obtain a summary statistic. To account for post_IRS transience in the value of a measure, I consier post-IRS to start 1 year after the IRS has ended.

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Selection vs. Neutral vs. Generalized immunity

As the ulimate goal is to understand the role that population structure plays in the resiliene of the population, the next step is to compare the response of the population under different scenarios. In essence, this repeats the above analysis above for the neutral and generalized immunity cases, and then comapres the three scenarios.

Time series of measure variables

First, let’s take a look how the time series of several measure variables in each of the 4 experiments change with scenario.

Time and probability to extinction

Our previous findings suggested that immune selection promotes the persistence of the parasite population across interventions. In that case we expect that the time and probability of extinction would be higher in the immune selection case.

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Quantitative effect of IRS in different scenarios

Again, calculate the ratio between pre- and post-IRS of a given measure variable, in the different scenarios. Only scenarios that did not go extinct appear. That is why the neutral scenario never appears because all runs always go extinct. Generally speaking we can see a stronger effect of IRS on populations with immune selection (red line is below orange line)

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